Surface gravity is the defining difference between
extrasolar giant planets and brown dwarfs, and to date is the only proven difference, although there are great hopes for metallicity.
Field brown dwarfs (hereafter BDs) have high surface gravities (\(g\)  of order \(10^{5}\)  cm/s\(^2\) ) and therefore very compressed scale heights.
Extrasolar giant planets (EGPs) have modest surface gravities (\(g\)  of order \(10^3\)  cm/s\(^2\) ) and extended scale heights [1]}, [2]}We do not intend to wade into the nomenclature battles here. For our purposes companion objects below \(\sim 13\,\rm M_J\)  are planets..
A BD and a self-luminous EGP of the same composition and the same effective temperature will have similar optical depths as a function of temperature, at least in the absence of clouds;
i.e., the function \(T(\tau )\)  is roughly the same. However, because \(p \propto \tau g\) ,
the BD has a much higher pressure at a given optical depth than does the EGP, and a BD is much cooler than the EGP at a given pressure.
Because lower temperatures and higher pressure favor CH\(_4\)  in its struggle with CO,
it has been pointed out that CH\(_4\)  will be more easily seen and CO less easily seen at lower gravity in BDs [3]}.
Hence [4]} suggested that the even lower gravity of HR8799b might be why no methane is seen in it.
We agree.
We will verify that the dependence on \(g\)  is strong and leads to qualitatively different outcomes for BDs and self-luminous EGPs,
a result implicit in previous work but far from fully appreciated.
